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BEGIN:VEVENT
SUMMARY:Opening
DTSTART;VALUE=DATE-TIME:20191106T130000Z
DTEND;VALUE=DATE-TIME:20191106T131500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-1@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/1/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solving Matrix Equations via Empirical Gramians
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-34@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Christian Himpe (Max Planck Institute for Dynamics o
f Complex Technical Systems)\nIn system theory\, the so-called system Gram
ian matrices are operators encoding certain properties of an underlying in
put-output system. Usually\, these system Gramians are computed as solutio
ns to matrix equations\, such as the Lyapunov equation and Sylvester equat
ion. This means\, the solution to certain matrix equations coincides with
these system Gramians. Now\, if the system Gramians are computable by othe
r means than matrix equations\, they still represent solutions to matrix e
quations. Empirical Gramians are such an alternative for system Gramian co
mputation\, which are based on their system-theoretic operator definition\
, and practically obtained via quadrature.\nThis contribution explores the
connection between matrix equations\, system Gramians and empirical Grami
ans\, and proposes empirical Gramians as potential solver for matrix equat
ions.\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contributions/34/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dynamical low-rank approximation of (skew-)symmetric matrices.
DTSTART;VALUE=DATE-TIME:20191108T085000Z
DTEND;VALUE=DATE-TIME:20191108T091500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-14@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Gianluca Ceruti (University of Tuebingen)\, Christia
n Lubich (University of Tuebingen)\nDynamical low-rank approximation is in
troduced and a numerical integrator that computes a symmetric or skew-sym
metric low-rank approximation to large symmetric or skew-symmetric time-de
pendent matrices that are either given explicitly or are the unknown solut
ion to a matrix differential equation is presented. We show that low-rank
time-dependent matrices are reproduced exactly\, and the error behaviour i
s robust to the presence of small singular values of the solution or the a
pproximate solution. The proposed structure preserving integrator and his
properties are then extended to (anti-)symmetric low-rank Tucker tensors.\
nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contributions/14/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rational Krylov for Stieltjes matrix functions: convergence and po
le selection
DTSTART;VALUE=DATE-TIME:20191108T101000Z
DTEND;VALUE=DATE-TIME:20191108T103500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-16@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Stefano Massei (EPF Lausanne)\, Leonardo Robol (Univ
ersity of Pisa)\nEvaluating the action of a matrix function on a vector\,
that is $x=f(\\mathcal M)v$\, is an ubiquitous task in applications. When
the matrix $\\mathcal M$ is large\, subspace projection method\, such as t
he rational Krylov method\, are usually employed. \nIn this work\, we pro
vide a quasi-optimal pole choice for rational Krylov methods applied to th
is task when $f(z)$ is either Cauchy-Stieltjes or Laplace-Stieltjes (or\,
which is equivalent\, completely monotonic) for a positive definite matrix
$\\mathcal M$. \n \nThen\, we consider the case when the argument $\\mat
hcal M$ has the Kronecker structure $\\mathcal M=I \\otimes A - B^T \\otim
es I$\, and is applied to a vector obtained vectorizing a low-rank matrix.
This finds application\, for instance\, in solving fractional diffusion e
quation on rectangular domains. \nWe introduce an error analysis for the n
umerical approximation of $x$. Pole choices and explicit convergence bound
s are given also in this case.\nhttps://indico3.mpi-magdeburg.mpg.de/event
/2/contributions/16/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A matrix equation method for solving PDE-constrained optimization
problems
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-39@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Alexandra Bünger (TU Chemnitz)\, Martin Stoll (TU C
hemnitz)\, Valeria Simoncini ( Alma Mater Studiorum\, Universita’ di Bol
ogna)\nPDE-constrained optimization problems arise in a broad number of ap
plications. The resulting large-scale saddle-point systems are challenging
to solve and acquiring a full solution is often infeasible. We present a
new framework to find a low-rank approximation to the solution by reformul
ating the system into a system of Sylvester-like matrix equations. These m
atrix equations are subsequently projected onto a small subspace via ratio
nal Krlyov-subspace iterations and we obtain a reduced problem by imposing
a Galerkin condition on its residual. In our presentation we discuss impl
ementation details and dependence on the problem parameters. Numerical exp
eriments will illustrate the performance of the new strategy.\nhttps://ind
ico3.mpi-magdeburg.mpg.de/event/2/contributions/39/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Model Reduction of Differential-Algebraic Systems by Parameter-Dep
endent Balanced Truncation
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-35@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Matthias Voigt (Uni Hamburg and TU Berlin)\, Jennife
r Przybilla (Max Planck Institute for Dynamics of Complex Technical System
s)\nWe deduce a procedure to use balanced truncation for parameter-depende
nt differential-algebraic systems. For this\, we have to solve parameter-d
ependent Lyapunov equations. Since solving large-scale Lyapunov equations
for every parameter leads to very high computational costs we utilize the
reduced-basis method to get a reduced Lyapunov equation that we can solve
instead. In order to use this method\, we first make the matrix pencil of
the system strictly dissipative to apply error estimators in the reduced b
asis method. Additionally\, we deal with the algebraic parts of the system
by using projections that lead to ordinary differential equations.\nhttps
://indico3.mpi-magdeburg.mpg.de/event/2/contributions/35/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M-M.E.S.S.-2.0 -- The “Matrix Equations\, Sparse Solvers”-tool
box for MATLAB® and GNU Octave
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-36@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Jens Saak (Max Planck Institute for Dynamics of Comp
lex Technical Systems)\nAmong other things\, M.E.S.S. can solve Lyapunov a
nd Riccati equations\, and perform model reduction of systems in state spa
ce and structured differential algebraic form. While until version 1.0.1 t
he work focused on algebraic equations and autonomous differential Riccati
equations (DREs)\, the latest release adds support also for non-autonomou
s DREs.\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contributions/36/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Solution of the Nonsymmetric T-Riccati Equation
DTSTART;VALUE=DATE-TIME:20191107T082500Z
DTEND;VALUE=DATE-TIME:20191107T085000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-57@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Davide Palitta (Max Planck Institute for Dynamics of
Complex Technical Systems)\, Peter Benner (Max Planck Institute for Dynam
ics of Complex Technical Systems)\nWe consider the nonsymmetric T-Riccati
equation \n\n$$\n0 = \\mathcal{R}_T(X):=DX+X^TA-X^TBX+C\,\\qquad (1)\n$$\n
\nwhere $A\,B\,C\,D\\in\\mathbb{R}^{n\\times n}$ and sufficient conditions
for the existence and uniqueness of a minimal (w.r.t. entry-wise comparis
on) solution $X_{\\min}\\in\\mathbb{R}^{n\\times n}$ are provided. To date
\, the nonlinear matrix equation (1) is still an unexplored problem in num
erical analysis and both theoretical results and computational methods are
lacking in the literature. We provide some sufficient conditions for the
existence and uniqueness of a nonnegative minimal solution and discuss its
efficient computation. Both the small-scale and the large-scale settings
are addressed and Newton-Kleinman-like methods are derived. The convergenc
e of these procedures\nto the minimal solution is proved and several numer
ical results illustrate the computational efficiency of the proposed metho
ds.\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contributions/57/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Graph Analysis with Laplacian Matrix Equations
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-17@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Eugenio Angriman (Humboldt-Universität zu Berlin)\,
Alexander van der Grinten (Humboldt-Universität zu Berlin)\, Maria Preda
ri (Humboldt-Universität zu Berlin)\, Henning Meyerhenke (Humboldt-Univer
sität zu Berlin)\nGraph (or network) analysis is concerned with knowledge
discovery from graph data. Corresponding analysis methods usually have th
eir roots in graph theory\, matrix computations\, and statistics.\n\nA gro
wing class of analysis algorithms consists of methods based on the graph's
Laplacian matrix. These include traditional methods using Laplacian eigen
vectors such as spectral partitioning\, spectral clustering\, or spectral
embedding. In the past 10-15 years\, Laplacian linear systems received sig
nificant interest in the context of graph analysis as well. They have appl
ications in graph partitioning\, graph sparsification\, electrical network
s\, and graph robustness\, to name just a few.\n\nOur poster focuses on La
placian linear systems in the context of centrality measures. Centrality m
easures indicate the importance of a node (or edge) in the graph based on
its position and belong to the most important analysis methods. Typically\
, they assign a real number to each node (or edge)\, which yields a rankin
g. On the poster we review (i) the state of the art concerning efficient a
lgorithms for computing Laplacian-based centrality measures and (ii) descr
ibe recent and ongoing work on accelerating such algorithms. We also portr
ay briefly our implementation of the Lean Algebraic Multigrid (LAMG) solve
r in NetworKit\, our growing open-source software for large-scale graph/ne
twork analysis.\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contribution
s/17/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Closing
DTSTART;VALUE=DATE-TIME:20191108T110000Z
DTEND;VALUE=DATE-TIME:20191108T111500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-59@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Peter Benner\, Bruno Iannazzo\nhttps://indico3.mpi-m
agdeburg.mpg.de/event/2/contributions/59/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Factored-form matrix sign iteration via principal pivot transforms
DTSTART;VALUE=DATE-TIME:20191108T103500Z
DTEND;VALUE=DATE-TIME:20191108T110000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-20@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Federico Poloni (University of Pisa)\, Peter Benner
(Max Planck Institute for Dynamics of Complex Technical Systems)\nWe descr
ibe a way to implement the matrix sign iteration $H_{k+1} = \\frac12 (H_k^
{\\mathstrut}+H_k^{-1})$ on a dense Hamiltonian matrix of the form \n\n$$H
_k = \\begin{bmatrix}A_k & B_kB_k^T\\\\ C_k^TC_k & -A_k^T & \\end{bmatrix}
$$\n\nin such a way that the blocks in positions $(1\,2)$ and $(2\,1)$ are
kept in low-rank factored form. The algorithm operates on their generator
s $B_k$ and $C_k$ directly\, and relies on principal pivot transforms (PPT
s) as its main building block\; more specifically it makes use of the fram
ework for factored-form PPTs in [Poloni\, Strabic 2016]. We discuss the st
ability properties of the resulting algorithm\, as well as applications th
at make use of the low-rank factors directly.\nhttps://indico3.mpi-magdebu
rg.mpg.de/event/2/contributions/20/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Differential Riccati Equation - A Galerkin Approach
DTSTART;VALUE=DATE-TIME:20191107T103500Z
DTEND;VALUE=DATE-TIME:20191107T110000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-22@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Peter Benner\, Maximilian Behr (Max Planck Institute
for Dynamics of Complex Technical Systems)\, Jan Heiland (Max Planck Inst
itute for Dynamics of Complex Technical Systems)\nWe consider the differen
tial Riccati equation\,\n$$\\dot{X} = A^T X + X A - X BB^T X + C^T C.$$\n\
nThe differential Riccati equation as well as the algebraic Riccati equati
on play important roles in applied mathematics like control theory and sys
tem theory. In our talk\, we focus on the large-scale case. The numerical
solution of these equation is challenging\, in particular\, because of the
enormous amount of storage. A general approach\, that has led to several
algorithms\, bases on an invariant subspace $Q \\subseteq \\mathbb R^{n\\t
imes n}$ such that $X(t) \\in Q$ for all $t$. After identifying a suitable
invariant subspace\, we develop a Galerkin approach for the numerical sol
ution of the differential Riccati equation. We review Davison-Maki method
s for the numerical solution of the resulting equation.\nhttps://indico3.m
pi-magdeburg.mpg.de/event/2/contributions/22/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergodicity coefficients for stochastic tensors
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-21@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Dario Fasino (University of Udine)\nA stochastic cub
ical tensor is a three-mode array (or hypermatrix) with nonnegative entrie
s\, whose $1$-mode fibers (i.e.\, columns) sum up to $1$. Such tensors app
ear in certain higher-order Markov chains and random walks with memory\, e
xactly as stochastic matrices describe classical discrete Markov chains an
d random walks.\nThe interest in higher-order stochastic processes is sign
ificantly growing in recent years as they are much better at modeling high
dimensional data and nonlinear dynamics in numerous applications. However
\, fundamental questions such as the convergence of the process towards a
limiting distribution and the uniqueness of such a limit are still not wel
l understood and are the subject of a rich recent literature.\nWe introduc
e a set of ergodicity coefficients for stochastic cubical tensors\, by ext
ending certain definitions known in the matrix case to the tensor setting.
The proposed coefficients yield new explicit formulas that \n(a) guarante
e the uniqueness of nonlinear Perron eigenvectors of stochastic tensors\,
\n(b) provide bounds on the sensitivity of such eigenvectors with respect
to changes in the tensor and \n(c) ensure the convergence of various highe
r-order Markov chains to the stationary distribution. \nJoint work with Fr
ancesco Tudisco.\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contributio
ns/21/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solving Matrix Equations with the MORLAB Toolbox
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-40@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Steffen Werner (Max Planck Institute for Dynamics of
Complex Technical Systems)\, Peter Benner (Max Planck Institute for Dynam
ics of Complex Technical Systems)\nThe MORLAB\, Model Order Reduction LABo
ratoy\, toolbox [1] is a free and open source software solution in MATLAB
and GNU Octave for linear model reduction problems. Providing system theor
etic model order reduction methods\, the basis of the highly efficient imp
lementation is built by a large variety of dense matrix equation solvers b
ased on iterative methods like the matrix sign function\, Newton or square
d Smith iterations\, and many more. Therefore\, the toolbox can be used to
solve continuous- or discrete-time Lyapunov\, Sylvester and Riccati equat
ions\, as well as continuous-time Bernoulli equations in a lot of differen
t formats and formulations.\n\n\n**References**\n [1] P. Benner and S. W.
R. Werner.\nMORLAB -- Model Order Reduction LABoratory (version 5.0)\, 201
9. \nSee also http://www.mpi-magdeburg.mpg.de/projects/morlab. \n doi:10.5
281/zenodo.3332716\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contribut
ions/40/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riccati and Lure equations associated with Port-Hamiltonian system
s
DTSTART;VALUE=DATE-TIME:20191108T094500Z
DTEND;VALUE=DATE-TIME:20191108T101000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-25@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Volker Mehrmann (TU Berlin)\nPort-Hamiltonian (pH) s
ystems are a very important modeling structure for large classes of techni
cal systems. In the optimal control problem for pH systems\, the resulting
boundary value problems and Lure/Riccati/Lyapunov have a double structure
.\nIt is a big challenge to make use of this double structure inan effecti
ve way\, but also in the solution of the associated structured eigenvalue
problems. We will present the theory\, first approaches\, and major open q
uestions\, in particular for the case of pH descritor systems.\nhttps://in
dico3.mpi-magdeburg.mpg.de/event/2/contributions/25/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matrix Integral Equations Arising in Parametric Model Order Reduct
ion
DTSTART;VALUE=DATE-TIME:20191108T082500Z
DTEND;VALUE=DATE-TIME:20191108T085000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-33@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Jens Saak (Max Planck Institute for Dynamics of Comp
lex Technical Systems)\, Tim Mitchell (Max Planck Institute for Dynamics o
f Complex Technical Systems)\, Manuela Hund (Max Planck Institute for Dyna
mics of Complex Technical Systems)\, Petar Mlinarić (Max Planck Institute
for Dynamics of Complex Technical Systems)\nWe consider $\\mathcal{H}_2 \
\otimes \\mathcal{L}_2$-optimal model order reduction of parametric linear
time-invariant dynamical systems\, where coupled matrix integral equation
s arise in the first-order necessary conditions (FONC). The quality of the
reduced-order model is measured using the $\\mathcal{H}_2$ norm for the p
arametric system\, which is averaged in the $\\mathcal{L}_2$-norm over the
parameter domain. \n\nWe motivate the FONC and aim to satisfy them using
an optimization-based approach that involves solving sequences of small-sc
ale Lyapunov equations and tall and skinny Sylvester equations.\nhttps://i
ndico3.mpi-magdeburg.mpg.de/event/2/contributions/33/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riccati-Feedback for a Class of Structured DAEs
DTSTART;VALUE=DATE-TIME:20191107T094500Z
DTEND;VALUE=DATE-TIME:20191107T101000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-13@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Jens Saak (Max Planck Institute for Dynamics of Comp
lex Technical Systems)\, Peter Benner\, Björn Baran (Max Planck Institute
for Dynamics of Complex Technical Systems)\nOur goal is the feedback stab
ilization of a two-dimensional two-phase Stefan problem coupled with (Navi
er-)Stokes equations. The Stefan problem can model solidification and melt
ing of pure materials and gets its name from the purely algebraic Stefan c
ondition which describes the coupling between the temperature of the mater
ial and its melting process.\n\nAfter linearization and discretization\, t
he stabilization problem results in a non-autonomous differential Riccati
equation (DRE) with differential-algebraic structure. While the actual in
dex of the resulting DAE needs further investigation\, the problem feature
s a structure that combines that of semi-explicit index-1 DAEs (resulting
from the Stefan condition) and Stokes-type index-2 DAEs (resulting from th
e dynamics of the convection).\n\nMoreover\, the interface between the two
phases in the domain evolves over time\, which causes all coefficients of
the resulting DRE to be time-varying. Thus\, existing DRE solvers have to
be adapted to this highly non-autonomous case which has significantly inc
reased computational costs and memory requirements.\n\nWe present techniqu
es to treat the specific structure of this coupled problem \nin the solver
for the DREs and show first results of the application of our feedback st
abilization.\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contributions/1
3/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matrix equations. Application to PDEs
DTSTART;VALUE=DATE-TIME:20191107T123000Z
DTEND;VALUE=DATE-TIME:20191107T125500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-41@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Valeria Simoncini (Universita di Bologna)\nMatrix eq
uations have arisen as the natural setting for various PDE discretization
methods such as finite differences\, isogeometric analysis\, spectral and
finite elements.\nThanks to major recent computational advances\, solving
certain classes of linear matrix equations is a competitive alternative to
dealing with the large (vector) linear systems classically stemming from
the aforementioned discretizations. In this talk we support these consider
ations with examples from the numerical treatment of possibly time-depende
nt PDE problems.\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contributio
ns/41/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:An efficient model reduction strategy for discrete-time index-2 d
escriptor control systems
DTSTART;VALUE=DATE-TIME:20191107T125500Z
DTEND;VALUE=DATE-TIME:20191107T132000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-26@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Ekram Hossain Khan (North South University)\, Moham
mad Sahadet Hossain (North South University)\, Sufi Galib Omar (North Sou
th University)\nIn this paper\, we present an efficient algorithm for mode
l reduction of discrete-time index-2 descriptor systems arising in context
of linear time invariant (LTI) control and stability of descriptor system
s. We propose a balanced truncation based model order reduction (MOR) stra
tegy which consists of two stages. In the first stage\, we reformulate the
descriptor system into a generalized system by manipulating its system st
ructure. Once the reformulated generalized system is obtained\, it is appl
icable for a balanced truncation-based model order reduction strategy. The
second stage of our work focuses is on a MOR method where the descriptor
system does not require to be transformed into the generalized system. Rat
her\, the balanced truncation MOR method can directly be applied on the in
dex-2 descriptor system. We also implement a Smith based iterative method
to compute the solutions of the Lyapunov equations corresponding to the tr
ansformed system without having to compute the projection matrices. Result
s from various numerical simulations are included to verify the high perfo
rmance and accuracy of our proposed algorithm.\nhttps://indico3.mpi-magde
burg.mpg.de/event/2/contributions/26/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A new Riccati ADI method
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-23@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Heike Faßbender (TU Braunschweig)\, Christian Bertr
am (TU Braunschweig)\nConsider the algebraic Riccati equation\n$$A^{*}X +
XA + C^*C - XBB^{*}X = 0$$\nwith large and sparse $A\\in \\mathbb{C}^{n\\t
imes n}$ and $B\\in \\mathbb{C}^{n\\times m}$\, $C\\in \\mathbb{C}^{p\\tim
es n}$. The goal is to find an approximate solution $X$ such that the rank
of the Riccati residual remains equal to $p$. A method to determine an ap
proximate solution to Riccati equations with this rank property is given b
y the RADI method [1]\, a generalization of the ADI method for linear matr
ix equations.\n\nWe present a new approach in which solves with $(A^*-\\mu
I_n)$ and the explicitly known residual factors are sufficient to obtain
the unique low-rank residual solution.\n\n\n[1] Benner\, P.\, Bujanović\,
Z.\, Kürschner\, P. et al. RADI: a low-rank ADI-type algorithm for large
scale algebraic Riccati equations. Numer. Math. (2018) 138: 301. https://
doi.org/10.1007/s00211-017-0907-5\nhttps://indico3.mpi-magdeburg.mpg.de/ev
ent/2/contributions/23/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:New-Type Matrix Equations Arising in Model-Order Reduction: State-
of-the-Art and Challenges
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-38@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Peter Benner (Max Planck Institute for Dynamics of C
omplex Technical Systems)\, Igor Pontes Duff (Max Planck Institute for Dyn
amics of Complex Technical Systems)\, Pawan Goyal (Max Planck Institute fo
r Dynamics of Complex Technical Systems)\nMatrix equations and their solut
ions play a key role in several problems arising in science and engineerin
g. Our primary focus lies on matrix equations appearing in model-order red
uction problems\, where several well-known procedures\, such as balanced t
runcation and interpolation-based methods\, can be set up in the matrix eq
uations form. In the last five years\, several model reduction schemes fo
r various classes of systems have been proposed. These classes include qua
dratic-bilinear\, polynomial\, switched systems and quadratic output syste
ms. The newly proposed MOR schemes for these classes require to solve par
ticular types of matrix equations. In this poster\, we provide an overview
of the MOR methods and the newly arising matrix equations. Furthermore\,
we discuss the current methods to solve these matrix equations and the cha
llenges in a large-scale setting.\nhttps://indico3.mpi-magdeburg.mpg.de/ev
ent/2/contributions/38/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matrices and tensors for polynomial rootfinding
DTSTART;VALUE=DATE-TIME:20191106T152500Z
DTEND;VALUE=DATE-TIME:20191106T155000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-27@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Patrick Kürschner (KU Leuven\, ESAT/STADIUS & Campu
s Kulak Kortrijk)\, Lieven De Lathauwer (KU Leuven\, ESAT/STADIUS)\nWe dis
cuss the problem of computing roots of systems of multivariate polynomials
by approaches from numerical linear and multilinear algebra.The key conce
pt in our approach is the Macaulay matrix\, a large and highly structured
matrix that contains the coefficients of the polynomials systems. The root
s can be retrieved from the nullspace of this matrix. We then show how thi
s root retrieval can be carried out using tensors and\, in particular\, te
nsor decompositions.\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contrib
utions/27/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A parameter-dependent smoother for the multigrid method
DTSTART;VALUE=DATE-TIME:20191106T150000Z
DTEND;VALUE=DATE-TIME:20191106T152500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-28@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Christian Löbbert (RWTH Aachen)\, Lars Grasedyck (R
WTH Aachen)\, Tim Werthmann (RWTH Aachen)\, Maren Klever\nWe prove the con
vergence of the multigrid method for parameter-dependent symmetric positiv
e definite linear systems. We present the smoothing and approximation prop
erties for such problems and prove the smoothing property for the paramete
r-dependent damped Richardson as well as the parameter-dependent damped Ja
cobi method.\nOur theoretical results require a parameter-dependent repres
entation of the operator\, the solution\, the right-hand side\, the smooth
er as well as the prolongation and restriction. We use tensor formats to d
erive such a representation for linear systems with affine-linear operator
s. For the parameter-dependent damped Jacobi method\, we derive an approxi
mation using exponential sums and prove the smoothing property for this re
presentation.\nIn numerical experiments\, we observe that the convergence
behavior of the multigrid method with the damped Jacobi smoother in the pa
rameter-dependent case seems to be grid size independent.\nhttps://indico3
.mpi-magdeburg.mpg.de/event/2/contributions/28/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matrix Equations Appearing in Parameter-dependent Fluid-structure
Interaction Discretizations
DTSTART;VALUE=DATE-TIME:20191107T140000Z
DTEND;VALUE=DATE-TIME:20191107T160000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-24@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Peter Benner (Max Planck Institute for Dynamics of C
omplex Technical Systems\, Magdeburg)\, Thomas Richter (Otto von Guericke
University Magdeburg)\, Roman Weinhandl (Otto von Guericke University Magd
eburg)\nIn the first place\, the poster presented will give an overview on
the matrix equations that appear in the low-rank parameter-dependent flui
d-structure interaction (FSI) framework. In contrast to linear FSI problem
s\, the equations that result after finite element discretization of param
eter-dependent nonlinear FSI problems are not translatable to a single mat
rix equation. Such a discretization with respect to $m \\in N$ shear modu
li given by the set $\\{\\mu_i\\}_{i \\in \\{1\,...\,m\\}} \\subset R$ and
a number of $n \\in N$ degrees of freedom yields equations of the form\n\
n$(A_0+\\mu_iA_1+A_2(x_i) )x_i=b \\quad \\text{for} \\quad i \\in \\{1\,.
..\,m\\}$\,\n\nwith $A_0$\, $A_1$\, $A_2(x_i) \\in R^{n \\times n}$\, $b \
\in R^n$ and the finite element solution $x_i \\in R^n$. $A_2(\\cdot)$ is
a discretization matrix of nonlinear operators and depends on the unknown.
An equivalent translation of the $m$ equations above to a matrix equation
\, similar to the linear case\, is not possible anymore. The poster will\,
in addition\, illustrate how such parameter-dependent nonlinear FSI discr
etizations can be tackled on the basis of the Newton iteration.\nhttps://i
ndico3.mpi-magdeburg.mpg.de/event/2/contributions/24/
LOCATION:Main/groundfloor-none - Magistrale (Max Planck Institute for Dyna
mics of Complex Technical Systems)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the efficient solution of large-scale algebraic Riccati equatio
ns with banded data
DTSTART;VALUE=DATE-TIME:20191107T085000Z
DTEND;VALUE=DATE-TIME:20191107T091500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-11@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Davide Palitta (Max Planck Institute for Dynamics of
Complex Technical Systems)\, Valeria Simoncini (Alma Mater Studiorum\, Un
iversita' di Bologna)\nThe numerical solution of the algebraic Riccati mat
rix equation \n$$(1)\\quad A^T X + XA − XSX + Q = 0\,$$\n\nwhere $A$\, $
S$\, $Q\\in\\mathbb{R}^{n\\times n}$ \, is an interesting and still challe
nging task especially when the problem dimension is very large\, say $n >
10^4$ \, as the dense solution $X$ cannot be store and a memory-saving app
roximation has to be sought.\n\nA vast portion of the literature focuses o
n the case of low-rank $S$ and $Q$ and many\, diverse solution schemes hav
e been developed to tackle this kind of equations. See\, e.g.\, [1] and th
e references therein. In particular\, the so-called low-rank methods compu
te a low-rank approximation to the exact solution $X$ in order to moderate
the memory requirements of the adopted algorithm.\n\nBy exploiting novel
results about the solution of Lyapunov equations with non low-rank right-h
and side [2\,3]\, a Newton iteration for (1) with a rank-structured $Q$ ha
s been recently proposed [4]. However\, also in such a scheme the matrix $
S$ is still supposed to be low-rank.\n\nIn this talk we consider Riccati e
quations with banded\, full-rank coefficent matrices $A$\, $S$ and $Q$ and
\, by taking inspiration from some early results by Incertis [5]\, a fresh
solution procedure that efficiently computes memory-saving approximate so
lutions is proposed. In particular\, the structure of the computed solutio
n $\\tilde X$ depends on some properties of the matrices $A$ and $Q$ and w
e can represent $\\tilde X$ in terms of either a banded matrix or a banded
plus low-rank matrix maintaining a very low storage demand of the overall
solution process.\n\nSeveral numerical results are reported to illustrate
the potential of the discussed method.\n\n**References**\n[1] P. Benner\,
Z. Bujanovic\, P. Kürschner and J. Saak. A numerical comparison of solve
rs for large-scale\, continuous-time algebraic Riccati equations. ArXiv Pr
eprint: 1811.00850\, 2018.\n[2] D. Palitta and V. Simoncini. Numerical met
hods for large-scale Lyapunov equations with symmetric banded data. SIAM J
ournal on Scientific Computing\, 40 (5): A3581–A3608\, 2018.\n[3] S. Mas
sei\, D. Palitta and L. Robol. Solving rank structured Sylvester and Lyapu
nov equations. SIAM Journal on Matrix Analysis and Applications\, 39 (4):
1564–1590\, 2018.\n[4] D. Kressner\, S. Massei and L. Robol. Low-rank up
dates and a divide-and-conquer method for linear matrix equations. SIAM Jo
urnal on Scientific Computing\, 41 (2): A848–A876\, 2019.\n[5] F. C. Inc
ertis. A new formulation of the algebraic Riccati equation problem. IEEE T
ransactions on Automatic Control\, 26 (3): 768–770\, 1981.\nhttps://indi
co3.mpi-magdeburg.mpg.de/event/2/contributions/11/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Order reduction methods for solving large-scale differential matri
x Riccati equations
DTSTART;VALUE=DATE-TIME:20191107T101000Z
DTEND;VALUE=DATE-TIME:20191107T103500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-31@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Valeria Simoncini (Alma Mater Studiorum\, Universita
' di Bologna)\, Gerhard Kirsten ( Alma Mater Studiorum\, Universita’ di
Bologna)\nWe consider the numerical solution of large-scale\, differential
matrix Riccati equations (DRE). Projection methods have recently arisen a
s a promising class of solution strategies. Existing approaches in this cl
ass focus on polynomial or extended Krylov subspaces as approximation spac
e. We show that great computational and memory advantages are obtained wit
h fully rational Krylov subspaces and we discuss several crucial issues su
ch as efficient time stepping and stopping criteria. Numerical experiments
illustrate the procedure's effectiveness.\nhttps://indico3.mpi-magdeburg.
mpg.de/event/2/contributions/31/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tensor-Train Decomposition for image classification
DTSTART;VALUE=DATE-TIME:20191106T155000Z
DTEND;VALUE=DATE-TIME:20191106T161500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-32@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Domitilla Brandoni (Alma Mater Studiorum\, Universit
a’ di Bologna)\, Valeria Simoncini ( Alma Mater Studiorum\, Universita
’ di Bologna)\nAutomatic Face Recognition has become increasingly import
ant in the past few years due to its several applications in daily life. N
umerical linear algebra tools have been extensively used for classificatio
n purposes. However\, since several factors can affect the image\, multili
near algebra tools seem to be a natural choice to deal with image classifi
cation. \n\nWe propose a new algorithm based on Tensor-Train Decomposition
and we compare it with other related methods\, such as the ones based on
SVD and HOSVD (High-Order Singular Value Decomposition).\nhttps://indico3.
mpi-magdeburg.mpg.de/event/2/contributions/32/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tensor numerical modeling of the collective electrostatic potentia
ls of many-particle systems
DTSTART;VALUE=DATE-TIME:20191106T140500Z
DTEND;VALUE=DATE-TIME:20191106T143000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-29@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Peter Benner (Max Planck Institute for Dynamics of C
omplex Technical Systems)\, Boris Khoromskij (Max-Planck Institute for Mat
hematics in the Sciences\, Leipzig)\, Matthias Stein (Max Planck Institute
for Dynamics of Complex Technical Systems)\, Venera Khoromskaia (Max-Plan
ck Institute for Mathematics in the Sciences\, Leipzig)\, Cleophas Kweyu (
Max Planck Institute for Dynamics of Complex Technical Systems)\nWe consid
er the rank-structured tensor approach for numerical modeling of long-rang
e potentials in many-particle systems. The method of grid-based assembled
tensor summation of the electrostatic potentials on 3D finite lattices [3]
exhibits the computational complexity of the order of $O(L)$ which is muc
h less than $O(L^3)$ in traditional Ewald-type summation.\n\nNovel range-s
eparated (RS) tensor format [4] applies to many-particle systems of genera
l type. These can be the free space electrostatic potentials of large biom
olecules or the multidimensional scattered data modeled by radial basis fu
nctions. The main advantage of the RS tensor format is that the rank of th
e canonical/Tucker tensor representing the sum of long range contributions
from all particles in the collective potential depends only logarithmical
ly on the number of particles $N$. The basic tool for calculation of the R
S tensor representation is the reduced higher order SVD (RHOSVD) introduce
d in [5]. The representation complexity of the short range part is $O(N)$
with a small prefactor independent on the number of particles. The interac
tion energies and forces of the many-particle system can be computed by us
ing only the long-range part of the collective potential\, with representa
tion complexity $O(n \\mathrm{log} N )$\, where n is the univariate grid s
ize.\n\nThe new regularization scheme for the Poisson-Boltzmann equation (
PBE) describing the electrostatic potential in biomolecules is based on th
e RS tensor representation to the discretized Dirac delta [2]. It leads to
solving a single system of FDM/FEM equations only for the smooth long-ran
ge part of the initially singular right-hand side of the PBE [1]. The resu
lting solution of PBE is the sum of the long- and short-range parts\, wher
e the latter is precomputed by the direct tensor summations\, without solv
ing the PBE. The numerical examples are presented.\n\n[1] P. Benner\, V. K
horomskaia\, B. N. Khoromskij\, C. Kweyu and M. Stein. Computing Electrost
atic Potentials of Biomolecules using Regularization based on the Range-se
parated Tensor Format. arXiv:1901.09864\, 2019.\n[2] Boris N. Khoromskij.
Tensor Numerical Methods in Scientific Computing. De Gruyter\, Berlin\, 20
18.\n[3] Venera Khoromskaia and Boris N. Khoromskij. Tensor Numerical Meth
ods in Quantum Chemistry. De Gruyter\, Berlin\, 2018.\n[4] P. Benner\, V.
Khoromskaia and B. N. Khoromskij. Range-Separated Tensor Format for Many-p
article Modeling. SIAM J Sci. Comput.\, 40 (2)\, A1034–A1062\, 2018.\n[5
] B. N. Khoromskij and V. Khoromskaia. Multigrid Tensor Approximation of F
unction Related Arrays. SIAM J Sci. Comput.\, 31(4)\, 3002-3026\, 2009.\nh
ttps://indico3.mpi-magdeburg.mpg.de/event/2/contributions/29/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quadratic matrix equations arising in two-dimensional random walks
DTSTART;VALUE=DATE-TIME:20191107T132000Z
DTEND;VALUE=DATE-TIME:20191107T134500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-18@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Jie Meng (Pusan National University)\, Leonardo Robo
l (University of Pisa)\, Stefano Massei (EPF Lausanne)\, Beatrice Meini (U
niversity of Pisa)\, Dario Andrea Bini (University of Pisa)\nThe treatment
of two-dimensional random walks in the quarter plane leads to Markov proc
esses which involve semi-infinite matrices having Toeplitz or block Toepli
tz structure plus a low-rank correction. In particular\, finding the stead
y state probability distribution requires computing the minimal nonnegativ
e solution of the quadratic matrix equation $A_1X^2+A_0X+A_{-1}=X$\, where
the coefficients $A_i$\, $i=-1\,0\,1$\, are semi-infinite nonnegative mat
rices\, which are Toeplitz except for a low-rank correction.\n\nWe introd
uce the sets $\\mathcal{QT}^d$ and $\\mathcal{EQT}$ of semi-infinite matri
ces with bounded infinity norm [2]. The former is made by matrices represe
ntable as a sum of a Toeplitz matrix and a compact correction with columns
having entries which decay to zero. The latter is formed by matrices in $
\\mathcal{QT}^d$ plus a further correction of the kind $ev^T$ for $e^T=(1\
,1\,\\ldots)$ and $v=(v_i)_{i\\in Z^+}$ such that $\\sum_{i=1}^\\infty |v_
i|\nhttps://indico3.mpi-magdeburg.mpg.de/event/2/contributions/18/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guaranteed a posteriori error bounds for low rank tensor approxima
te solutions
DTSTART;VALUE=DATE-TIME:20191106T134000Z
DTEND;VALUE=DATE-TIME:20191106T140500Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-19@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Sergey Dolgov (University of Bath\, UK)\, Tomas Vejc
hodsky (Institute of Mathematics\, Czech Academy of Sciences)\nWe propose
guaranteed and fully computable upper bound on the energy norm of the erro
r in low rank Tensor Train (TT) approximate solutions of (possibly) high d
imensional reaction-diffusion problems. The error bound is obtained from E
uler-Lagrange equations for a complementary flux reconstruction problem\,
which are solved in the low rank TT representation using the block Alterna
ting Linear Scheme. This bound is guaranteed to be above the energy norm o
f the total error\, including the discretization error\, the tensor approx
imation error\, and the error in the solver of linear algebraic equations.
Numerical examples with the Poisson equation and the Schroedinger equatio
n with the Henon-Heiles potential in up to 40 dimensions will be presented
to illustrate the efficiency of this approach.\nhttps://indico3.mpi-magde
burg.mpg.de/event/2/contributions/19/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Effective Partitioning and Communication Strategies for Parallel S
parse Tensor Factorization
DTSTART;VALUE=DATE-TIME:20191106T131500Z
DTEND;VALUE=DATE-TIME:20191106T134000Z
DTSTAMP;VALUE=DATE-TIME:20211203T215400Z
UID:indico-contribution-15@indico3.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Oguz Kaya (Université Paris-Saclay and Laboratoire
de Recherche en Informatique (LRI))\nSparse tensor decompositions have bec
ome increasingly popular in the literature due to their capability to natu
rally model high dimensional sparse data with many features\, and glean hi
dden relations owing to underlying low-rank structures within the data. Th
ey have been successfully employed in many application settings including
recommender systems\, graph analytics\, healthcare data analytics\, web se
arch\, cyber security\, and many others. The aptitude of tensor methods fo
r such big data analysis applications solicited the development of efficie
nt parallel tensor factorization algorithms capable of handling datasets o
f billions of entries\, which has been among the most trending areas of re
search in the HPC community in the recent past.\n\nIn this talk\, we will
discuss parallelization techniques for sparse tensor factorization togethe
r with various partitioning strategies for balancing computation/memory co
sts and reducing communication. We will compare advantages and limitations
of various approaches and touch upon outstanding challenges for better pa
rallel scalability. We will conclude the talk with an overview of the capa
bilities of the PACOS library (PArtitioning and COmmunication framework fo
r Sparse irregular applications) that enable devising efficient and scalab
le parallel sparse tensor factorization kernels as well as partitioning ro
utines\, and facilitate reproducibility of scalability results.\nhttps://i
ndico3.mpi-magdeburg.mpg.de/event/2/contributions/15/
LOCATION:Prigogine (MPI Magdeburg)
URL:https://indico3.mpi-magdeburg.mpg.de/event/2/contributions/15/
END:VEVENT
END:VCALENDAR